DFT/electrostatic calculations of pK(a) values in cytochrome c oxidase

Structural and functional mechanisms of cytochrome c oxidase

Cytochrome c oxidase (CcO) is the terminal enzyme in the electron transfer chain in mitochondria. It catalyzes the four-electron reduction of O2 to H2O and harnesses the redox energy to drive unidirectional proton translocation against a proton electrochemical gradient. A great deal of research has been conducted to comprehend the molecular properties of CcO. However, the mechanism by which the oxygen reduction reaction is coupled to proton translocation remains poorly understood. Here, we review the chemical properties of a variety of key oxygen intermediates of bovine CcO (bCcO) revealed by time-resolved resonance Raman spectroscopy and the structural features of the enzyme uncovered by serial femtosecond crystallography, an innovative technique that allows structural determination at room temperature without radiation damage. The implications of these data on the proton translocation mechanism are discussed.

Reaction pathways, proton transfer, and proton pumping in ba3 class cytochrome c oxidase: perspectives from DFT quantum chemistry and molecular dynamics

After drawing comparisons between the reaction pathways of cytochrome c oxidase (CcO, Complex 4) and the preceding complex cytochrome bc1 (Complex 3), both being proton pumping complexes along the electron transport chain, we provide an analysis of the reaction pathways in bacterial ba3 class CcO, comparing spectroscopic results and kinetics observations with results from DFT calculations. For an important arc of the catalytic cycle in CcO, we can trace the energy pathways for the chemical protons and show how these pathways drive proton pumping of the vectorial protons. We then explore the proton loading network above the Fe heme a3-CuB catalytic center, showing how protons are loaded in and then released by combining DFT-based reaction energies with molecular dynamics simulations over states of that cycle. We also propose some additional reaction pathways for the chemical and vector protons based on our recent work with spectroscopic support.

Lipid-Dependent Titration of Glutamic Acid at a Bilayer Membrane Interface

The ionization properties of protein side chains in lipid-bilayer membranes will differ from the canonical values of side chains exposed to an aqueous solution. While the propensities of positively charged side chains of His, Lys, and Arg to release a proton in lipid membranes have been rather well characterized, the propensity for a negatively charged Glu side chain to receive a proton and achieve the neutral state in a bilayer membrane has been less well characterized. Indeed, the ionization of the glutamic acid side chain has been predicted to depend on its depth of burial in a lipid membrane but has been difficult to verify experimentally. To address the issue, we incorporated an interfacial Glu residue at position 4 of a distinct 23-residue transmembrane helix and used ²H NMR to examine the helix properties as a function of pH. We observe that the helix tilt and azimuthal rotation vary little with pH, but the extent of helix unraveling near residues 3 and 4 changes as the Glu residue E4 titrates. Remarkably, the ²H quadrupolar splitting for the side chain of alanine A3 responds to pH with an apparent pK _a of 4.8 in 1,2-dilauroyl-sn-glycero-3-phosphocholine (DLPC) and 6.3 in 1,2-dimyristoyl-sn-glycero-3-phosphatidylcholine (DMPC), but is unchanged up to pH 8.0 in 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) in the presence of residue E4. With bilayers composed of alkali-stable ether-linked lipids, the side chain of A3 responds to pH with an apparent pK _a of 11.0 in the ether analogue of DOPC. These results suggest that the depth dependence of Glu ionization in lipid-bilayer membranes may be steeper than previously predicted or envisioned.

Influence of glutamic acid residues and pH on the properties of transmembrane helices

Negatively charged side chains are important for the function of particular ion channels and certain other membrane proteins. To investigate the influence of single glutamic acid side chains on helices that span lipid-bilayer membranes, we have employed GWALP23 (acetyl-GGALW⁵LALALALALALALW¹⁹LAGA-amide) as a favorable host peptide framework. We substituted individual Leu residues with Glu residues (L12E or L14E or L16E) and incorporated specific ²H-labeled alanine residues within the core helical region or near the ends of the sequence. Solid-state ²H NMR spectra reveal little change for the core labels in GWALP23-E12, -E14 and -E16 over a pH range of 4 to 12.5, with the spectra being broader for samples in DOPC compared to DLPC bilayers. The spectra for samples with deuterium labels near the helix ends on alanines 3 and 21 show modest pH-dependent changes in the extent of unwinding of the helix terminals in DLPC and DOPC bilayers. The combined results indicate minor overall responses of these transmembrane helices to changes in pH, with the most buried residue E12 showing no pH dependence. While the Glu residues E14 and E16 may have high pK_a values in the lipid bilayer environment, it is also possible that a paucity of helix response is masking the pK_a values. Interestingly, when E16 is present, spectral changes at high pH report significant local unwinding of the core helix. Our results are consistent with the expectation that buried carboxyl groups aggressively hold their protons and/or waters of hydration.

The CO Photodissociation and Recombination Dynamics of the W172Y/F282T Ligand Channel Mutant of Rhodobacter sphaeroides aa3 Cytochrome c Oxidase

In the ligand channel of the cytochrome c oxidase from Rhodobacter sphaeroides (Rs aa3 ) W172 and F282 have been proposed to generate a constriction that may slow ligand access to and from the active site. To explore this issue, the tryptophan and phenylalanine residues in Rs aa3 were mutated to the less bulky tyrosine and threonine residues, respectively, which occupy these sites in Thermus thermophilus (Tt) ba3 cytochrome oxidase. The CO photolysis and recombination dynamics of the reduced wild-type Rs aa3 and the W172Y/F282T mutant were investigated using time-resolved optical absorption spectroscopy. The spectral changes associated with the multiple processes are attributed to different conformers. The major CO recombination process (44 μs) in the W172Y/F282T mutant is ~500 times faster than the predominant CO recombination process in the wild-type enzyme (~23 ms). Classical dynamic simulations of the wild-type enzyme and double mutant showed significant structural changes at the active site in the mutant, including movement of the heme a3 ring-D propionate toward CuB and reduced binuclear center cavity volume. These structural changes effectively close the ligand exit pathway from the binuclear center, providing a basis for the faster CO recombination in the double mutant.

Current advances in research of cytochrome c oxidase

The function of cytochrome c oxidase as a biomolecular nanomachine that transforms energy of redox reaction into protonmotive force across a biological membrane has been subject of intense research, debate, and controversy. The structure of the enzyme has been solved for several organisms; however details of its molecular mechanism of proton pumping still remain elusive. Particularly, the identity of the proton pumping site, the key element of the mechanism, is still open to dispute. The pumping mechanism has been for a long time one of the key unsolved issues of bioenergetics and biochemistry, but with the accelerating progress in this field many important details and principles have emerged. Current advances in cytochrome oxidase research are reviewed here, along with a brief discussion of the most complete proton pumping mechanism proposed to date, and a molecular basis for control of its efficiency.

Modeling and computations of the intramolecular electron transfer process in the two-heme protein cytochrome c(4)

The di-heme protein Pseudomonas stutzeri cytochrome c(4) (cyt c(4)) has emerged as a useful model for studying long-range protein electron transfer (ET). Recent experimental observations have shown a dramatically different pattern of intramolecular ET between the two heme groups in different local environments. Intramolecular ET in homogeneous solution is too slow (>10 s) to be detected but fast (ms-μs) intramolecular ET in an electrochemical environment has recently been achieved by controlling the molecular orientation of the protein assembled on a gold electrode surface. In this work we have performed computational modeling of the intramolecular ET process by a combination of density functional theory (DFT) and quantum mechanical charge transfer theory to disclose reasons for this difference. We first address the electronic structures of the model heme core with histidine and methionine axial ligands in both low- and high-spin states by structure-optimized DFT. The computations enable estimating the intramolecular reorganization energy of the ET process for different combinations of low- and high-spin heme couples. Environmental reorganization free energies, work terms ("gating") and driving force were determined using dielectric continuum models. We then calculated the electronic transmission coefficient of the intramolecular ET rate using perturbation theory combined with the electronic wave functions determined by the DFT calculations for different heme group orientations and Fe-Fe separations. The reactivity of low- and high-spin heme groups was notably different. The ET rate is exceedingly low for the crystallographic equilibrium orientation but increases by several orders of magnitude for thermally accessible non-equilibrium configurations. Deprotonation of the propionate carboxyl group was also found to enhance the ET rate significantly. The results are discussed in relation to the observed surface immobilization effect and support the notion of conformationally gated ET.

Coupled electron and proton transfer reactions during the O→E transition in bovine cytochrome c oxidase

A combined DFT/electrostatic approach is employed to study the coupling of proton and electron transfer reactions in cytochrome c oxidase (CcO) and its proton pumping mechanism. The coupling of the chemical proton to the internal electron transfer within the binuclear center is examined for the O→E transition. The novel features of the His291 pumping model are proposed, which involve timely well-synchronized sequence of the proton-coupled electron transfer reactions. The obtained pK(a)s and E(m)s of the key ionizable and redox-active groups at the different stages of the O→E transition are consistent with available experimental data. The PT step from E242 to H291 is examined in detail for various redox states of the hemes and various conformations of E242 side-chain. Redox potential calculations of the successive steps in the reaction cycle during the O→E transition are able to explain a cascade of equilibria between the different intermediate states and electron redistribution between the metal centers during the course of the catalytic activity. All four electrometric phases are discussed in the light of the obtained results, providing a robust support for the His291 model of proton pumping in CcO.

Similarity of cytochrome c oxidases in different organisms

Most of biological oxygen reduction is catalyzed by the heme-copper oxygen reductases. These enzymes are redox-driven proton pumps that take part in generating the proton gradient in both prokaryotes and mitochondria that drives synthesis of ATP. The enzymes have been divided into three evolutionarily-related groups: the A-, B-, and C-families. Recent comparative studies suggest that all oxygen reductases perform the same chemistry for oxygen reduction and comprise the same essential elements of the proton pumping mechanism, such as the proton loading and kinetic gating sites, which, however, appear to be different in different families. All species of the A-family, however, demonstrate remarkable similarity of the central processing unit of the enzyme, as revealed by their recent crystal structures. Here we demonstrate that cytochrome c oxidases (CcO) of such diverse organisms as a mammal (bovine heart mitochondrial CcO), photosynthetic bacteria (Rhodobacter sphaeroides CcO), and soil bacteria (Paracoccus denitrificans CcO) are not only structurally similar, but almost identical in microscopic electrostatics and thermodynamics properties of their key amino-acids. By using pK(a) calculations of some of the key residues of the catalytic site, D- and K- proton input, and putative proton output channels of these three different enzymes, we demonstrate that the microscopic properties of key residues are almost identical, which strongly suggests the same mechanism in these species. The quantitative precision with which the microscopic physical properties of these enzymes have remained constant despite different evolutionary routes undertaken is striking.

B3LYP study on reduction mechanisms from O2 to H2O at the catalytic sites of fully reduced and mixed-valence bovine cytochrome c oxidases

Reduction mechanisms of oxygen molecule to water molecules in the fully reduced (FR) and mixed-valence (MV) bovine cytochrome c oxidases (CcO) have been systematically examined based on the B3LYP calculations. The catalytic cycle using four electrons and four protons has been also shown consistently. The MV CcO catalyses reduction to produce one water molecule, while the FR CcO catalyses to produce two water molecules. One water molecule is added into vacant space between His240 and His290 in the catalytic site. This water molecule constructs the network of hydrogen bonds of Tyr244, farnesyl ethyl, and Thr316 that is a terminal residue of the K-pathway. It plays crucial roles for the proton transfer to the dioxygen to produce the water molecules in both MV and FR CcOs. Tyr244 functions as a relay of the proton transfer from the K-pathway to the added water molecule, not as donors of a proton and an electron to the dioxygen. The reduction mechanisms of MV and FR CcOs are strictly distinguished. In the FR CcO, the Cu atom at the Cu(B) site maintains the reduced state Cu(I) during the process of formation of first water molecule and plays an electron storage. At the final stage of formation of first water molecule, the Cu(I) atom releases an electron to Fe-O. During the process of formation of second water molecule, the Cu atom maintains the oxidized state Cu(II). In contrast with experimental proposals, the K-pathway functions for formation of first water molecule, while the D-pathway functions for second water molecule. The intermediates, P(M), P(R), F, and O, obtained in this work are compared with those proposed experimentally.

Microscopic pKa analysis of Glu286 in cytochrome c oxidase (Rhodobacter sphaeroides): toward a calibrated molecular model

As stringent tests for the molecular model and computational protocol, microscopic pK(a) calculations are performed for the key residue, Glu286, in cytochrome c oxidase (CcO) using a combined quantum mechanical/molecular mechanical (QM/MM) potential and a thermodynamic integration protocol. The impact of the number of water molecules in the hydrophobic cavity and protonation state of several key residues (e.g., His334, Cu(B)-bound water, and PRD(a3)) on the computed microscopic pK(a) values of Glu286 has been systematically examined. To help evaluate the systematic errors in the QM/MM-based protocol, microscopic pK(a) calculations have also been carried out for sites in a soluble protein (Asp70 in T4 lysozyme) and a better-characterized membrane protein (Asp85 in bacteriorhodopsin). Overall, the results show a significant degree of internal consistency and reproducibility that support the effectiveness of the computational framework. Although the number of water molecules in the hydrophobic cavity does not greatly influence the computed pK(a) of Glu286, the protonation states of several residues, some of which are rather far away, have more significant impacts. Adopting the standard protonation state for all titratable residues leaves a large net charge on the system and a significantly elevated pK(a) for Glu286, highlighting that any attempt to address the energetics of proton transfers in CcO at a microscopic level should carefully select the protonation state of residues, even those not in the immediate neighborhood of the active site. The calculations indirectly argue against the deprotonation of His334 for the proton pumping process, although further studies that explicitly compute its pK(a) are required for a more conclusive statement. Finally, the deprotonated Glu286 is found to be in a stable water-mediated connection with PRD(a3) for at least several nanoseconds when this presumed pumping site is protonated. This does not support the proposed role of Glu286 as a robust gating valve that prevents proton leakage, although a conclusive statement awaits a more elaborate characterization of the Glu286-PRD(a3) connectivity with free energy simulations and a protonated PRD(a3). The large sets of microscopic simulations performed here have provided useful guidance to the establishment of a meaningful molecular model and effective computational protocol for explicitly analyzing the proton transfer kinetics in CcO, which is required for answering key questions regarding the pumping function of this fascinating and complex system.

Communication between R481 and Cu(B) in cytochrome bo(3) ubiquinol oxidase from Escherichia coli

The R481 residue of cytochrome bo(3) ubiquinol oxidase from E. coli is highly conserved in the heme-copper oxidase superfamily. It has been postulated to serve as part of a proton loading site that regulates proton translocation across the protein matrix of the enzyme. Along these lines, proton pumping efficiency has been demonstrated to be abolished in many R481 mutants. However, R481Q in bo(3) from E. coli has been shown to be fully functional, implying that the positive charge of the arginine is not required for proton translocation [ Puustinen , A. and Wikstrom , M. ( 1999 ) Proc. Natl. Acad. Sci. U.S.A. 96 , 35 - 37 ]. In an effort to delineate the structural role of R481 in the bo(3) oxidase, we used resonance Raman spectroscopy to compare the nonfunctional R481L mutant and the functional R481Q mutant, to the wild type protein. Resonance Raman data of the oxidized and reduced forms of the R481L mutant indicate that the mutation introduces changes to the heme o(3) coordination state, reflecting a change in position and/or coordination of the Cu(B) located on the distal side of heme o(3), although it is approximately 10 A away from R481. In the reduced-CO adduct of R481L, the frequencies of the Fe-CO and C-O stretching modes indicate that, unlike the wild type protein, the Cu(B) is no longer close to the heme-bound CO. In contrast, resonance Raman data obtained from the various oxidation and ligation states of the R481Q mutant are similar to those of the wild type protein, except that the mutation causes an enhancement of the relative intensity of the beta conformer of the CO-adduct, indicating a shift in the equilibrium between the alpha and beta conformers. The current findings, together with crystallographic structural data of heme-copper oxidases, indicate that R481 plays a keystone role in stabilizing the functional structure of the Cu(B) site through a hydrogen bonding network involving ordered water molecules. The implications of these data on the proton translocation mechanism are considered.

The chemistry of the CuB site in cytochrome c oxidase and the importance of its unique His-Tyr bond

The CuB metal center is at the core of the active site of the heme-copper oxidases, comprising a copper atom ligating three histidine residues one of which is covalently bonded to a tyrosine residue. Using quantum chemical methodology, we have studied the CuB site in several redox and ligand states proposed to be intermediates of the catalytic cycle. The importance of the His-Tyr crosslink was investigated by comparing energetics, charge, and spin distributions between systems with and without the crosslink. The His-Tyr bond was shown to decrease the proton affinity and increase the electron affinity of both Tyr-244 and the copper. A previously unnoticed internal electronic equilibrium between the copper atom and the tyrosine was observed, which seems to be coupled to the unique structure of the system. In certain states the copper and Tyr-244 compete for the unpaired electron, the localization of which is determined by the oxygenous ligand of the copper. This electronic equilibrium was found to be sensitive to the presence of a positive charge 10 A away from the center, simulating the effect of Lys-319 in the K-pathway of proton transfer. The combined results provide an explanation for why the heme-copper oxidases need two pathways of proton uptake, and why the K-pathway is active only in the second half of the reaction cycle.

Dielectric relaxation of cytochrome c oxidase: Comparison of the microscopic and continuum models

We have studied a charge-insertion process that models the deprotonation of a histidine side chain in the active site of cytochrome c oxidase (CcO) using both the continuum electrostatic calculations and the microscopic simulations. The group of interest is a ligand to Cu(B) center of CcO, which has been previously suggested to play the role of the proton pumping element in the enzyme; the group is located near a large internal water cavity in the protein. Using the nonpolarizable Amber-99 force field in molecular dynamics (MD) simulations, we have calculated the nuclear part of the reaction-field energy of charging of the His group and combined it with the electronic part, which we estimated in terms of the electronic continuum (EC) model, to obtain the total reaction-field energy of charging. The total free energy obtained in this MDEC approach was then compared with that calculated using pure continuum electrostatic model with variable dielectric parameters. The dielectric constant for the "dry" protein and that of the internal water cavity of CcO were determined as those parameters that provide best agreement between the continuum and microscopic MDEC model. The nuclear (MD) polarization alone (without electronic part) of a dry protein was found to correspond to an unphysically low dielectric constant of only about 1.3, whereas the inclusion of electronic polarizability increases the protein dielectric constant to 2.6-2.8. A detailed analysis is presented as to how the protein structure should be selected for the continuum calculations, as well as which probe and atomic radii should be used for cavity definition. The dielectric constant of the internal water cavity was found to be 80 or even higher using "standard" parameters of water probe radius, 1.4 A, and protein atomic radii from the MD force field for cavity description; such high values are ascribed to the fact that the standard procedure produces unphysically small cavities. Using x-ray data for internal water in CcO, we have explored optimization of the parameters and the algorithm of cavity description. For Amber radii, the optimal probe size was found to be 1.25 A; the dielectric of water cavity in this case is in the range of 10-16. The most satisfactory cavity description, however, was achieved with ProtOr atomic radii, while keeping the probe radius to be standard 1.4 A. In this case, the value of cavity dielectric constant was found to be in the range of 3-6. The obtained results are discussed in the context of recent calculations and experimental measurements of dielectric properties of proteins.

Toward a chemical mechanism of proton pumping by the B-type cytochrome c oxidases: application of density functional theory to cytochrome ba3 of Thermus thermophilus

A mechanism for proton pumping by the B-type cytochrome c oxidases is presented in which one proton is pumped in conjunction with the weakly exergonic, two-electron reduction of Fe-bound O 2 to the Fe-Cu bridging peroxodianion and three protons are pumped in conjunction with the highly exergonic, two-electron reduction of Fe(III)- (-)O-O (-)-Cu(II) to form water and the active oxidized enzyme, Fe(III)- (-)OH,Cu(II). The scheme is based on the active-site structure of cytochrome ba 3 from Thermus thermophilus, which is considered to be both necessary and sufficient for coupled O 2 reduction and proton pumping when appropriate gates are in place (not included in the model). Fourteen detailed structures obtained from density functional theory (DFT) geometry optimization are presented that are reasonably thought to occur during the four-electron reduction of O 2. Each proton-pumping step takes place when a proton resides on the imidazole ring of I-His376 and the large active-site cluster has a net charge of +1 due to an uncompensated, positive charge formally associated with Cu B. Four types of DFT were applied to determine the energy of each intermediate, and standard thermochemical approaches were used to obtain the reaction free energies for each step in the catalytic cycle. This application of DFT generally conforms with previously suggested criteria for a valid model (Siegbahn, P. E. M.; Blomberg, M. A. R. Chem. Rev. 2000, 100, 421-437) and shows how the chemistry of O 2 reduction in the heme a 3 -Cu B dinuclear center can be harnessed to generate an electrochemical proton gradient across the lipid bilayer.

A chemically explicit model for the mechanism of proton pumping in heme-copper oxidases

A mechanism for proton pumping is described that is based on chemiosmotic principles and the detailed molecular structures now available for cytochrome oxidases. The importance of conserved water positions and a step-wise gated process of proton translocation is emphasized, where discrete electron transfer events are coupled to proton uptake and expulsion. The trajectory of each pumped proton is the same for all four substrate electrons. An essential role for the His-Tyr cross-linked species is discussed, in gating of the D- and K-channels and as an acceptor/donor of electrons and protons at the binuclear center.

Glutamic acid 242 is a valve in the proton pump of cytochrome c oxidase

Aerobic life is based on a molecular machinery that utilizes oxygen as a terminal electron sink. The membrane-bound cytochrome c oxidase (CcO) catalyzes the reduction of oxygen to water in mitochondria and many bacteria. The energy released in this reaction is conserved by pumping protons across the mitochondrial or bacterial membrane, creating an electrochemical proton gradient that drives production of ATP. A crucial question is how the protons pumped by CcO are prevented from flowing backwards during the process. Here, we show by molecular dynamics simulations that the conserved glutamic acid 242 near the active site of CcO undergoes a protonation state-dependent conformational change, which provides a valve in the pumping mechanism. The valve ensures that at any point in time, the proton pathway across the membrane is effectively discontinuous, thereby preventing thermodynamically favorable proton back-leakage while maintaining an overall high efficiency of proton translocation. Suppression of proton leakage is particularly important in mitochondria under physiological conditions, where production of ATP takes place in the presence of a high electrochemical proton gradient.

Proton solvation and transport in aqueous and biomolecular systems: insights from computer simulations

The excess proton in aqueous media plays a pivotal role in many fundamental chemical (e.g., acid-base chemistry) and biological (e.g., bioenergetics and enzyme catalysis) processes. Understanding the hydrated proton is, therefore, crucial for chemistry, biology, and materials sciences. Although well studied for over 200 years, excess proton solvation and transport remains to this day mysterious, surprising, and perhaps even misunderstood. In this feature article, various efforts to address this problem through computer modeling and simulation will be described. Applications of computer simulations to a number of important and interesting systems will be presented, highlighting the roles of charge delocalization and Grotthuss shuttling, a phenomenon unique in many ways to the excess proton in water.

Single-ion solvation free energies and the normal hydrogen electrode potential in methanol, acetonitrile, and dimethyl sulfoxide

The division of thermodynamic solvation free energies of electrolytes into contributions from individual ionic constituents is conventionally accomplished by using the single-ion solvation free energy of one reference ion, conventionally the proton, to set the single-ion scales. Thus, the determination of the free energy of solvation of the proton in various solvents is a fundamental issue of central importance in solution chemistry. In the present article, relative solvation free energies of ions and ion-solvent clusters in methanol, acetonitrile, and dimethyl sulfoxide (DMSO) have been determined using a combination of experimental and theoretical gas-phase free energies of formation, solution-phase reduction potentials and acid dissociation constants, and gas-phase clustering free energies. Applying the cluster pair approximation to differences between these relative solvation free energies leads to values of -263.5, -260.2, and -273.3 kcal/mol for the absolute solvation free energy of the proton in methanol, acetonitrile, and DMSO, respectively. The final absolute proton solvation free energies are used to assign absolute values for the normal hydrogen electrode potential and the solvation free energies of other single ions in the solvents mentioned above.

Calculated proton uptake on anaerobic reduction of cytochrome C oxidase: is the reaction electroneutral?

Cytochrome c oxidase is a transmembrane proton pump that builds an electrochemical gradient using chemical energy from the reduction of O(2). Ionization states of all residues were calculated with Multi-Conformation Continuum Electrostatics (MCCE) in seven anaerobic oxidase redox states ranging from fully oxidized to fully reduced. One long-standing problem is how proton uptake is coupled to the reduction of the active site binuclear center (BNC). The BNC has two cofactors: heme a(3) and Cu(B). If the protein needs to maintain electroneutrality, then 2 protons will be bound when the BNC is reduced by 2 electrons in the reductive half of the reaction cycle. The effective pK(a)s of ionizable residues around the BNC are evaluated in Rhodobacter sphaeroides cytochrome c oxidase. At pH 7, only a hydroxide coordinated to Cu(B) shifts its pK(a) from below 7 to above 7 and so picks up a proton when heme a(3) and Cu(B) are reduced. Glu I-286, Tyr I-288, His I-334, and a second hydroxide on heme a(3) all have pK(a)s above 7 in all redox states, although they have only 1.6-3.5 DeltapK units energy cost for deprotonation. Thus, at equilibrium, they are protonated and cannot serve as proton acceptors. The propionic acids near the BNC are deprotonated with pK(a)s well below 7. They are well stabilized in their anionic state and do not bind a proton upon BNC reduction. This suggests that electroneutrality in the BNC is not maintained during the anaerobic reduction. Proton uptake on reduction of Cu(A), heme a, heme a(3), and Cu(B) shows approximately 2.5 protons bound per 4 electrons, in agreement with prior experiments. One proton is bound by a hydroxyl group in the BNC and the rest to groups far from the BNC. The electrochemical midpoint potential (E(m)) of heme a is calculated in the fully oxidized protein and with 1 or 2 electrons in the BNC. The E(m) of heme a shifts down when the BNC is reduced, which agrees with prior experiments. If the BNC reduction is electroneutral, then the heme a E(m) is independent of the BNC redox state.

Different types of biological proton transfer reactions studied by quantum chemical methods

Different types of proton transfer occurring in biological systems are described with examples mainly from ribonucleotide reductase (RNR) and cytochrome c oxidase (CcO). Focus is put on situations where electron and proton transfer are rather strongly coupled. In the long range radical transfer in RNR, it is shown that the presence of hydrogen atom transfer (HAT) is the most logical explanation for the experimental observations. In another example from RNR, it is shown that a transition state for concerted motion of both proton and electron can be found even if the donors are separated by a quite long distance. In CcO, the essential proton transfer for the OO bond cleavage, and the most recent modelings of proton translocation are described, indicating a few remaining major problems.

Combined DFT and electrostatics study of the proton pumping mechanism in cytochrome c oxidase

Cytochrome c oxidase is a redox-driven proton pump which converts atmospheric oxygen to water and couples the oxygen reduction reaction to the creation of a membrane proton gradient. The structure of the enzyme has been solved; however, the mechanism of proton pumping is still poorly understood. Recent calculations from this group indicate that one of the histidine ligands of enzyme's CuB center, His291, may play the role of the pumping element. In this paper, we report on the results of calculations that combined first principles DFT and continuum electrostatics to evaluate the energetics of the key energy generating step of the model-the transfer of the chemical proton to the binuclear center of the enzyme, where the hydroxyl group is converted to water, and the concerted expulsion of the proton from delta-nitrogen of His291 ligand of CuB center. We show that the energy generated in this step is sufficient to push a proton against an electrochemical membrane gradient of about 200 mV. We have also re-calculated the pKa of His291 for an extended model in which the whole Fe(a3)-CuB center with their ligands is treated by DFT. Two different DFT functionals (B3LYP and PBE0), and various dielectric models of the protein have been used in an attempt to estimate potential errors of the calculations. Although current methods of calculations do not allow unambiguous predictions of energetics in proteins within few pKa units, as required in this case, the present calculation provides further support for the proposed His291 model of CcO pump and makes a specific prediction that could be targeted in the experimental test.

Improved Density Functional Theory/Electrostatic Calculation of the His291 Protonation State in Cytochrome c Oxidase: Self-Consistent Charges for Solvation Energy Calculation

The protonation state of His291 in cytochrome c oxidase (CcO), a ligand to the Cu(B) center of the enzyme, has been recently studied in this group by using combined density functional theory (DFT)/electrostatic (QM/MM) calculations. On the basis of these calculations, a model of the proton pumping mechanism of CcO has been proposed. Due to certain technical difficulties, the procedure used in the previous calculation to find partial atomic charges of the QM system for the solvation energy evaluation was not entirely satisfactory; i.e., it was not self-consistent. Here, we describe a procedure that resolves the problem and report on the improved calculations of the protonation state of the His residue. The new procedure fits the protein and reaction field potentials in the region of the QM system with artificial point charges placed on a surface of a sphere surrounding the QM system and a few charges inside the sphere and allows one to perform DFT calculations that involve an inhomogeneous dielectric environment in a self-consistent way. The procedure improves the accuracy of calculations in comparison with previous work. The improved results show, however, that although the absolute energies change significantly the relative energies of the protonated and deprotonated states of His291 remain close to the previously reported ones and therefore do not change significantly the pK(a) values reported earlier. Therefore, our new improved calculations support for the proposed His291 model of the CcO pump.

Reduction of nitric oxide in bacterial nitric oxide reductase--a theoretical model study

The mechanism of the nitric oxide reduction in a bacterial nitric oxide reductase (NOR) has been investigated in two model systems of the heme-b(3)-Fe(B) active site using density functional theory (B3LYP). A model with an octahedral coordination of the non-heme Fe(B) consisting of three histidines, one glutamate and one water molecule gave an energetically feasible reaction mechanism. A tetrahedral coordination of the non-heme iron, corresponding to the one of Cu(B) in cytochrome oxidase, gave several very high barriers which makes this type of coordination unlikely. The first nitric oxide coordinates to heme b(3) and is partly reduced to a more nitroxyl anion character, which activates it toward an attack from the second NO. The product in this reaction step is a hyponitrite dianion coordinating in between the two irons. Cleaving an NO bond in this intermediate forms an Fe(B) (IV)O and nitrous oxide, and this is the rate determining step in the reaction mechanism. In the model with an octahedral coordination of Fe(B) the intrinsic barrier of this step is 16.3 kcal/mol, which is in good agreement with the experimental value of 15.9 kcal/mol. However, the total barrier is 21.3 kcal/mol, mainly due to the endergonic reduction of heme b(3) taken from experimental reduction potentials. After nitrous oxide has left the active site the ferrylic Fe(B) will form a mu-oxo bridge to heme b(3) in a reaction step exergonic by 45.3 kcal/mol. The formation of a quite stable mu-oxo bridge between heme b(3) and Fe(B) is in agreement with this intermediate being the experimentally observed resting state in oxidized NOR. The formation of a ferrylic non-heme Fe(B) in the proposed reaction mechanism could be one reason for having an iron as the non-heme metal ion in NOR instead of a Cu as in cytochrome oxidase.

Monte Carlo simulations of proton pumps: on the working principles of the biological valve that controls proton pumping in cytochrome c oxidase

Gaining a detailed understanding of the proton-pumping process in cytochrome c oxidase (COX) is one of the challenges of modern biophysics. Recent mutation experiments have highlighted this challenge by showing that a single mutation (the N139D mutation) blocks the overall pumping while continuing to channel protons to the binuclear center without inhibiting the oxidase activity. Rationalizing this result has been a major problem because the mutation is quite far from E286, which is believed to serve as the branching point for the proton transport in the pumping process. In the absence of a reasonable explanation for this important observation, we have developed a Monte Carlo simulation method that can convert mutation and structural information to pathways for proton translocation and simulate the pumping process in COX on a millisecond and even subsecond time scale. This tool allows us to reproduce and propose a possible explanation to the effect of the N139D mutation and to offer a consistent model for the origin of the "valve effect" in COX, which is crucial for maintaining uphill proton pumping. Furthermore, obtaining the first structure-based simulation of proton pumping in COX, or in any other protein, indicates that our approach should provide a powerful tool for verification of mechanistic hypotheses about the action of proton transport proteins.

Theoretical studies of enzyme mechanisms involving high-valent iron intermediates

Recent theoretical contributions to the elucidation of mechanisms for iron containing enzymes are reviewed. The method used in most of these studies is hybrid density functional theory with the B3LYP functional. Three classes of enzymes are considered, the mononuclear non-heme enzymes, enzymes containing iron dimers, and heme-containing enzymes. Mechanisms for both dioxygen and substrate activations are discussed. The reactions usually go through two half-cycles, where a high-valent intermediate Fe(IV)O species is created in the first half-cycle, and the substrate reactions involving this intermediate occur in the second half-cycle. Similarities between the three classes of enzymes dominate, but significant differences also exist.

Adding explicit solvent molecules to continuum solvent calculations for the calculation of aqueous acid dissociation constants

Aqueous acid dissociation free energies for a diverse set of 57 monoprotic acids have been calculated using a combination of experimental and calculated gas and liquid-phase free energies. For ionic species, aqueous solvation free energies were calculated using the recently developed SM6 continuum solvation model. This model combines a dielectric continuum with atomic surface tensions to account for bulk solvent effects. For some of the acids studied, a combined approach that involves attaching a single explicit water molecule to the conjugate base (anion), and then surrounding the resulting anion-water cluster by a dielectric continuum, significantly improves the agreement between the calculated pK(a) value and experiment. This suggests that for some anions, particularly those concentrating charge on a single exposed heteroatom, augmenting implicit solvent calculations with a single explicit water molecule is required, and adequate, to account for strong short-range hydrogen bonding interactions between the anion and the solvent. We also demonstrate the effect of adding several explicit waters by calculating the pK(a) of bicarbonate (HCO(3)(-)) using as the conjugate base carbonate (CO(3)(2-)) bound by up to three explicit water molecules.

Two conformational states of Glu242 and pKas in bovine cytochrome c oxidase

Cytochrome c oxidase (CcO) is the terminal enzyme in the respiratory electron transport chain of aerobic organisms. It catalyses the reduction of atmospheric oxygen to water, and couples this reaction to proton pumping across the membrane; this process generates the electrochemical gradient that subsequently drives the synthesis of ATP. The molecular details of the mechanism by which electron transfer is coupled to proton pumping in CcO is poorly understood. Recent calculations from our group indicate that His291, a ligand of the Cu(B) center of the enzyme, may play the role of the pumping element. In this paper we describe calculations in which a DFT/continuum electrostatic method is used to explore the coupling of the conformational changes of Glu242 residue, the main proton donor of both chemical and pump protons, to its pKa, and the pKa of His291, a putative proton loading site of our pumping model. The computations are done for several redox states of metal centers, different protonation states of Glu242 and His291, and two well-defined conformations of the Glu242 side chain. Thus, in addition to equilibrium redox/protonation states of the catalytic cycle, we also examine the transient and intermediate states. Different dielectric models are employed to investigate the robustness of the results, and their viability in the light of the proposed proton pumping mechanism of CcO. The main results are in agreement with the experimental measurements and support the proposed pumping mechanism. Additionally, the present calculations indicate a possibility of gating through conformational changes of Glu242; namely, in the pumping step, we find that Glu242 needs to be reprotonated before His291 can eject a proton to the P-site of membrane. As a result, the reprotonation of Glu can control proton release from the proton loading site.

A theoretical study on nitric oxide reductase activity in a ba3-type heme-copper oxidase

The mechanism of nitric oxide reduction in a ba(3)-type heme-copper oxidase has been investigated using density functional theory (B3LYP). Four possible mechanisms have been studied and free energy surfaces for the whole catalytic cycle including proton and electron transfers have been constructed by comparison to experimental data. The first nitric oxide coordinates to heme a(3) and is partly reduced having some nitroxyl anion character ((3)NO(-)), and it is thus activated toward the attack by the second N-O. In this reaction step a cyclic hyponitrous acid anhydride intermediate with the two oxygens coordinating to Cu(B) is formed. The cyclic hyponitrous acid anhydride is quite stable in a local minimum with high barriers for both the backward and forward reactions and should thus be observable experimentally. To break the N-O bond and form nitrous oxide, the hyponitrous acid anhydride must be protonated, the latter appearing to be an endergonic process. The endergonicity of the proton transfer makes the barrier of breaking the N-O bond directly after the protonation too high. It is suggested that an electron should enter the catalytic cycle at this stage in order to break the N-O bond and form N(2)O at a feasible rate. The cleavage of the N-O bond is the rate limiting step in the reaction mechanism and it has a barrier of 17.3 kcal/mol, close to the experimental value of 19.5 kcal/mol. The overall exergonicity is fitted to experimental data and is 45.6 kcal/mol.

Acidity of a Cu-Bound Histidine in the Binuclear Center of CytochromecOxidase

Cytochrome c oxidase (CcO) is a crucial enzyme in the respiratory chain. Its function is to couple the reduction of molecular oxygen, which takes place in the Fea3-CuB binuclear center, to proton translocation across the mitochondrial membrane. Although several high-resolution structures of the enzyme are known, the molecular basis of proton pumping activation and its mechanism remain to be elucidated. We examine a recently proposed scheme (J. Am. Chem. Soc. 2004, 126, 1858; FEBS Lett. 2004, 566, 126) that involves the deprotonation of the CuB-bound imidazole ring of a histidine (H291 in mammalian CcO) as a key element in the proton pumping mechanism. The central feature of that proposed mechanism is that the pKa values of the imidazole vary significantly depending on the redox state of the metals in the binuclear center. We use density functional theory in combination with continuum electrostatics to calculate the pKa values, successively in bulk water and within the protein, of the Cu-bound imidazole in various Cu- and Cu-Fe complexes. From pKas in bulk water, we derived a value of -266.34 kcal.mol(-1) for the proton solvation free energy (Delta). This estimate is in close agreement with the experimental value of -264.61 kcal.mol(-1) (J. Am. Chem. Soc. 2001, 123, 7314), which reinforces the conclusion that Delta is more negative than previous values used for pKa calculations. Our approach, on the basis of the study of increasingly more detailed models of the CcO binuclear center at different stages of the catalysis, allows us to examine successively the effect of each of the two metals' redox states and of solvation on the acidity of imidazole, whose pKa is approximately 14 in bulk water. This analysis leads to the following conclusions: first, the effect of Cu ligation on the imidazole acidity is negligible regardless of the redox state of the metal. Second, results obtained for Cu-Fe complexes in bulk water indicate that Cu-bound imidazole pKa values lie within the range of 14.8-16.6 throughout binuclear redox states corresponding to the catalytic cycle, demonstrating that the effect of the Fe oxidation states is also negligible. Finally, the low-dielectric CcO proteic environment shifts the acid-base equilibrium toward a neutral imidazole, further increasing the corresponding pKa values. These results are inconsistent with the proposed role of the Cu-bound histidine as a key element in the pumping mechanism. Limitations of continuum solvation models in pKa calculations are discussed.

Titration behavior of residues at the entrance of the D-pathway of cytochrome c oxidase from paracoccus denitrificans investigated by continuum electrostatic calculations

Continuum electrostatic calculations were employed to investigate the titration curves of the fully oxidized state of wild type and several variants of cytochrome c oxidase from Paracoccus denitrificans (N131D, N131C, N131V, and D124N) for different values of the dielectric constant of the protein. The effects of the mutations at the entrance of the D-proton transfer pathway were found to be quite localized to their immediate surroundings. The results can be well interpreted in the light of the available biochemical and structural data and help understanding the effects of mutations on proton conductivity. The mutations of aspartic acid Asp-I-124 to a neutral residue resulted in a decreased pK(a) value of His-I-28 suggesting that the mutation of His-I-28 may have a significant influence on the coupling of electron and proton transfer in cytochrome c oxidase. We also investigated the effect of the mutations N131D, N131C, and N131V on the residue Glu-I-278 in terms of its pK(a) value and electrostatic interaction energies.

Analysis of the kinetics of the membrane potential generated by cytochrome c oxidase upon single electron injection

In a recent work from this group (Popovic, D. M.; Stuchebrukhov A. A. FEBS Lett. 2004, 566, 126), a model of proton pumping by cytochrome c oxidase (CcO) was proposed. The key element of the model is His291 (bovine notation), a histidine ligand to enzyme's CuB redox center, which plays the role of the pump element. The model assumes that upon electron transfer between heme a and the binuclear catalytic center of the enzyme, two sequential proton transfers occur: First, a proton from Glu242 is transferred to an unprotonated His291, then a second proton, after reprotonation of Glu242 from the negative side of the membrane, is transferred to a hydroxyl group in the binuclear center, a water molecule is formed, and the first proton, due to proton-proton repulsion, is expelled from His291 to the positive side of the membrane, resulting in a pumping event. In the process the free energy of water formation (i.e., reduction of oxygen) is transformed into a proton gradient across the membrane. The model possesses specific kinetic features. It assumes, for example, that upon electron transfer the first proton is transferred to the proton-loading site of the pump, His291, and not to the catalytic center of the enzyme. Here, we analyze the kinetic properties of the proposed model, and calculate the time dependence of the membrane potential generated by CcO upon a single electron injection into the enzyme. These data are directly compared with recent experimental measurements of the membrane potential generated by CcO. Specifically, F to O, and O to E transitions will be discussed. Several enzymes from different organisms (bovine, two bacterial enzymes, and several mutants) are compared and discussed in detail. The kinetic description, however, is phenomenological, and does not include explicitly the nature of the groups involved in proton translocation, except in terms of their position depth within the membrane; thus, the kinetic equations developed here are in fact describe a generic model, similar, e.g., to that proposed earlier by Peter Rich (P.R. Rich, Towards an understanding of the chemistry of oxygen reduction and proton translocation in the iron-copper respiratory oxidases. Aust. J. Plant Physiol. 22 (1995) 479-486), and which is based on the idea of displacement of the pumped protons by the chemical ones.